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Running a backup is a very resource heavy process as, by definition, we need to read the entirety of the site's files and its database's contents.

The only thing you can possibly do is try to make the backup run slower. Whether that works depends on the resolution of the host's I/O usage metric. If they calculate it in realtime it'll be impossible taking a backup even manually unless you have a poor soul copying the site one file at a time over several days. If they calculate an average value every few seconds you can play with the Fine-tuning settings in the Configuration page. For example you could set:

Maximum execution time: 7 seconds

Minimum execution time: 3 seconds

Execution time bias: 50%

The backup would run between 1.5 to 3 seconds (that's min*bias to min), then wait for 4 to 5.5 seconds (the remainder of the time to the maximum execution time) doing absolutely nothing. That's an average of 30% duty cycle which means that the resource usage will drop around three times but also the backup will take three times more.

If the server calculates the I/O usage every second you could try

Maximum execution time: 7 seconds

Minimum execution time: 1 seconds

Execution time bias: 50%

This makes the backup about 10 times slower as it only runs 0.5 to 1 second and then waits for 6 to 6.5 seconds doing nothing.

Sure you could make it even slower with the settings 10/1/50 but at this point you might just as well ask the host to take a backup in stone tablets and deliver them by donkey.

Also note that these settings only apply for backups which are NOT taken with the native CRON CLI script or wp-cli. The alternative CRON script, legacy front-end backup, JSON API and backend backups will honour these timing settings.

I would also say that this kind of host is antithetical to the concept of taking backups and imposes unreasonable restrictions. I think you might be better off looking for different hosting which might actually also be cheaper. I recommend Rochen for reseller plans, Linode for self-service virtual servers. Full disclosure: Rochen gives us free of charge hosting for our business site but I'm also their paying client for reseller hosting which I am using for hosting sites unrelated to Akeeba Ltd.